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  • 1
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    Interpretable Neural Networks with Frank-Wolfe: Sparse Relevance Maps and Relevance Orderings (2022)
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    Publikationsdatum: 2024-01-12
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 2
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    Cutting Plane Selection with Analytic Centers and Multiregression (2022)
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    Publikationsdatum: 2024-01-12
    Beschreibung: Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 3
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    Complexity of near-optimal robust versions of multilevel optimization problems (2021)
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    Publikationsdatum: 2024-01-12
    Beschreibung: Near-optimality robustness extends multilevel optimization with a limited deviation of a lower level from its optimal solution, anticipated by higher levels. We analyze the complexity of near-optimal robust multilevel problems, where near-optimal robustness is modelled through additional adversarial decision-makers. Near-optimal robust versions of multilevel problems are shown to remain in the same complexity class as the problem without near-optimality robustness under general conditions.
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 4
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    How Many Clues To Give? A Bilevel Formulation For The Minimum Sudoku Clue Problem (2023)
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    Publikationsdatum: 2024-01-12
    Beschreibung: It has been shown that any 9 by 9 Sudoku puzzle must contain at least 17 clues to have a unique solution. This paper investigates the more specific question: given a particular completed Sudoku grid, what is the minimum number of clues in any puzzle whose unique solution is the given grid? We call this problem the Minimum Sudoku Clue Problem (MSCP). We formulate MSCP as a binary bilevel linear program, present a class of globally valid inequalities, and provide a computational study on 50 MSCP instances of 9 by 9 Sudoku grids. Using a general bilevel solver, we solve 95\% of instances to optimality, and show that the solution process benefits from the addition of a moderate amount of inequalities. Finally, we extend the proposed model to other combinatorial problems in which uniqueness of the solution is of interest.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 5
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    A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming (2023)
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    Publikationsdatum: 2024-01-12
    Beschreibung: The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 6
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    Branching via Cutting Plane Selection: Improving Hybrid Branching (2023)
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    Publikationsdatum: 2024-01-12
    Beschreibung: Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a 4% decrease in solve time, and an 8% decrease in number of nodes over affected instances of MIPLIB 2017.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
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    The SCIP Optimization Suite 8.0 (2021)
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    Publikationsdatum: 2024-01-12
    Beschreibung: The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 8.0 of the SCIP Optimization Suite. Major updates in SCIP include improvements in symmetry handling and decomposition algorithms, new cutting planes, a new plugin type for cut selection, and a complete rework of the way nonlinear constraints are handled. Additionally, SCIP 8.0 now supports interfaces for Julia as well as Matlab. Further, UG now includes a unified framework to parallelize all solvers, a utility to analyze computational experiments has been added to GCG, dual solutions can be postsolved by PaPILO, new heuristics and presolving methods were added to SCIP-SDP, and additional problem classes and major performance improvements are available in SCIP-Jack.
    Sprache: Englisch
    Materialart: reportzib , doc-type:preprint
    Format: application/pdf
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  • 8
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    Branching via Cutting Plane Selection: Improving Hybrid Branching (2023)
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    Publikationsdatum: 2024-01-24
    Beschreibung: Cutting planes and branching are two of the most important algorithms for solving mixed-integer linear programs. For both algorithms, disjunctions play an important role, being used both as branching candidates and as the foundation for some cutting planes. We relate branching decisions and cutting planes to each other through the underlying disjunctions that they are based on, with a focus on Gomory mixed-integer cuts and their corresponding split disjunctions. We show that selecting branching decisions based on quality measures of Gomory mixed-integer cuts leads to relatively small branch-and-bound trees, and that the result improves when using cuts that more accurately represent the branching decisions. Finally, we show how the history of previously computed Gomory mixed-integer cuts can be used to improve the performance of the state-of-the-art hybrid branching rule of SCIP. Our results show a $4\%$ decrease in solve time, and an $8\%$ decrease in number of nodes over affected instances of MIPLIB 2017.
    Sprache: Englisch
    Materialart: article , doc-type:article
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  • 9
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    A Context-Aware Cutting Plane Selection Algorithm for Mixed-Integer Programming (2023)
    Details
    Publikationsdatum: 2024-01-24
    Beschreibung: The current cut selection algorithm used in mixed-integer programming solvers has remained largely unchanged since its creation. In this paper, we propose a set of new cut scoring measures, cut filtering techniques, and stopping criteria, extending the current state-of-the-art algorithm and obtaining a 5\% performance improvement for SCIP over the MIPLIB 2017 benchmark set.
    Sprache: Englisch
    Materialart: conferenceobject , doc-type:conferenceObject
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  • 10
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    Improved Local Models and New Bell Inequalities Via Frank-Wolfe Algorithms (2023)
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    Publikationsdatum: 2024-01-24
    Beschreibung: In Bell scenarios with two outcomes per party, we algorithmically consider the two sides of the membership problem for the local polytope: Constructing local models and deriving separating hyperplanes, that is, Bell inequalities. We take advantage of the recent developments in so-called Frank-Wolfe algorithms to significantly increase the convergence rate of existing methods. First, we study the threshold value for the nonlocality of two-qubit Werner states under projective measurements. Here, we improve on both the upper and lower bounds present in the literature. Importantly, our bounds are entirely analytical; moreover, they yield refined bounds on the value of the Grothendieck constant of order three: 1.4367⩽KG(3)⩽1.4546. Second, we demonstrate the efficiency of our approach in multipartite Bell scenarios, and present local models for all projective measurements with visibilities noticeably higher than the entanglement threshold. We make our entire code accessible as a julia library called BellPolytopes.jl.
    Sprache: Englisch
    Materialart: article , doc-type:article
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